$\text{Group Action}:$
What is meant by $\text{coordinatewise complex conjugation}$ in group action ?
Do there there exists any concept of $\text{conjugation}$ in Group action ?
I am week in Group action theory.
This context is from my previous question on Group action here what is the action of $\operatorname{Aut}(\mathbb{Z})$ on $\mathbb{C}^n$, see the comment of @Arturo Magidin
Can someone explain it shortly with an example?
Judging without context, I presume your have some vector $(c_1, c_2, \dots, c_n) \in \mathbb C^n$. In this case, the componentwise complex conjugation will be $(c_1^*, c_2^*, \cdots, c_n^*) \in \mathbb C^n$, since you are conjugating the complex vector componentwise.